Regina Calculation Engine
Public Member Functions
regina::NTorusBundle Class Reference

Represents a torus bundle over the circle. More...

#include <manifold/ntorusbundle.h>

Inheritance diagram for regina::NTorusBundle:
regina::NManifold regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

 NTorusBundle ()
 Creates a new trivial torus bundle over the circle.
 NTorusBundle (const NMatrix2 &newMonodromy)
 Creates a new torus bundle over the circle using the given monodromy.
 NTorusBundle (long mon00, long mon01, long mon10, long mon11)
 Creates a new torus bundle over the circle using the given monodromy.
 NTorusBundle (const NTorusBundle &cloneMe)
 Creates a clone of the given torus bundle.
const NMatrix2getMonodromy () const
 Returns the monodromy describing how the upper and lower torus boundaries are identified.
NAbelianGroupgetHomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented.
std::ostream & writeName (std::ostream &out) const
 Writes the common name of this 3-manifold as a human-readable string to the given output stream.
std::ostream & writeTeXName (std::ostream &out) const
 Writes the common name of this 3-manifold in TeX format to the given output stream.
- Public Member Functions inherited from regina::NManifold
virtual ~NManifold ()
 A destructor that does nothing.
std::string getName () const
 Returns the common name of this 3-manifold as a human-readable string.
std::string getTeXName () const
 Returns the common name of this 3-manifold in TeX format.
std::string getStructure () const
 Returns details of the structure of this 3-manifold that might not be evident from its common name.
virtual NTriangulationconstruct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented.
bool operator< (const NManifold &compare) const
 Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold.
virtual std::ostream & writeStructure (std::ostream &out) const
 Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream.
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream.
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing.
virtual ~ShareableObject ()
 Default destructor that does nothing.
std::string toString () const
 Returns the output from writeTextShort() as a string.
std::string toStringLong () const
 Returns the output from writeTextLong() as a string.

Detailed Description

Represents a torus bundle over the circle.

This is expressed as the product of the torus and the interval, with the two torus boundaries identified according to some specified monodromy.

The monodromy is described by a 2-by-2 matrix M as follows. Let a and b be generating curves of the upper torus boundary, and let p and q be the corresponding curves on the lower torus boundary (so that a and p are parallel and b and q are parallel). Then we identify the torus boundaries so that, in additive terms:

     [a]       [p]
     [ ] = M * [ ]
     [b]       [q]
 

All optional NManifold routines except for construct() are implemented for this class.

Test:
Included in the test suite.
Todo:
Feature: Implement the == operator for finding conjugate and inverse matrices.

Constructor & Destructor Documentation

regina::NTorusBundle::NTorusBundle ( )
inline

Creates a new trivial torus bundle over the circle.

In other words, this routine creates a torus bundle with the identity monodromy.

regina::NTorusBundle::NTorusBundle ( const NMatrix2 newMonodromy)
inline

Creates a new torus bundle over the circle using the given monodromy.

Precondition:
The given matrix has determinant +1 or -1.
Parameters:
newMonodromydescribes precisely how the upper and lower torus boundaries are identified. See the class notes for details.
regina::NTorusBundle::NTorusBundle ( long  mon00,
long  mon01,
long  mon10,
long  mon11 
)
inline

Creates a new torus bundle over the circle using the given monodromy.

The four elements of the monodromy matrix are passed separately. They combine to give the full monodromy matrix M as follows:

           [ mon00  mon01 ]
     M  =  [              ]
           [ mon10  mon11 ]
 
Precondition:
The monodromy matrix formed from the given parameters has determinant +1 or -1.
Parameters:
mon00the (0,0) element of the monodromy matrix.
mon01the (0,1) element of the monodromy matrix.
mon10the (1,0) element of the monodromy matrix.
mon11the (1,1) element of the monodromy matrix.
regina::NTorusBundle::NTorusBundle ( const NTorusBundle cloneMe)
inline

Creates a clone of the given torus bundle.

Parameters:
cloneMethe torus bundle to clone.

Member Function Documentation

NAbelianGroup* regina::NTorusBundle::getHomologyH1 ( ) const
virtual

Returns the first homology group of this 3-manifold, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.

The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.

The homology group will be newly allocated and must be destroyed by the caller of this routine.

Returns:
the first homology group of this 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NManifold.

const NMatrix2 & regina::NTorusBundle::getMonodromy ( ) const
inline

Returns the monodromy describing how the upper and lower torus boundaries are identified.

See the class notes for details.

Returns:
the monodromy for this torus bundle.
std::ostream& regina::NTorusBundle::writeName ( std::ostream &  out) const
virtual

Writes the common name of this 3-manifold as a human-readable string to the given output stream.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
outthe output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NManifold.

std::ostream& regina::NTorusBundle::writeTeXName ( std::ostream &  out) const
virtual

Writes the common name of this 3-manifold in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Warning:
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; standard output will be used.
Parameters:
outthe output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NManifold.


The documentation for this class was generated from the following file:

Copyright © 1999-2012, The Regina development team
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).